RESONANCE AND ASYMPTOTIC SERIES BASED IDENTIFICATION OF AN ACOUSTICALLY RIGID SPHERE (SINGULARITY EXPANSION METHOD).

Abstract

Identification of the resonances and the local determination of the radius of curvature of an acoustically rigid sphere from simulated transient input-output data is presented. The scattering from the sphere is formulated using three techniques: the classic Mie-Lorenz series, the singularity expansion method (SEM), and the asymptotic series approximation. The Mie-Lorenz series is used to provide synthetic data. The SEM and the asymptotic series are used to develop two parametric inverse models. The scattered velocity potential is separated into three components: the reflection, the first creeping wave, and the second creeping wave. The effect of removing various components of the scattered potential on the resonance identification is shown, along with the effect of adding small amounts of noise. We find that the identification of a few resonances requires a relatively high order autoregressive, moving-average model. In addition, we show that removing the reflection from the synthetic output has only a small effect on the single or multiple output identified resonances. However, we find that changing the time origin, removing the second creeping wave, or adding small amounts of noise results in large errors in the identified resonances. We find that the radius of curvature can be accurately determined from synthetic data using the asymptotic series based identification. In addition, the identification is robust in the presence of noise, and requires only a low order asymptotic series model.